ScienceAges 10-12

Series & parallel resistor networks

Calculate equivalent resistance for resistors in series (R₁ + R₂) or in parallel ((R₁ × R₂) ÷ (R₁ + R₂)). Review suitability for your learners before teaching.

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Age band:Ages 10-12 Ages 13-15

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Worksheet StudioPractice pack · Ages 10-12

Series & parallel resistor networks

Take your time. Show your thinking.

1. Two resistors of 14 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 14 Ω, R₂ = 17 Ω · R_eq = R₁ + R₂ = ?
2. Two resistors of 32 Ω and 96 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 32 Ω ∥ 96 Ω · 1/R_eq = 1/32 + 1/96
3. Two resistors of 48 Ω and 144 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 48 Ω ∥ 144 Ω · 1/R_eq = 1/48 + 1/144
4. Two resistors of 24 Ω and 11 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 24 Ω, R₂ = 11 Ω · R_eq = R₁ + R₂ = ?
5. Two resistors of 2 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 2 Ω, R₂ = 14 Ω · R_eq = R₁ + R₂ = ?
6. Two resistors of 9 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 9 Ω, R₂ = 6 Ω · R_eq = R₁ + R₂ = ?
7. Two resistors of 17 Ω and 24 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 17 Ω, R₂ = 24 Ω · R_eq = R₁ + R₂ = ?
8. Two resistors of 3 Ω and 6 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 3 Ω ∥ 6 Ω · 1/R_eq = 1/3 + 1/6
9. Two resistors of 24 Ω and 72 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 24 Ω ∥ 72 Ω · 1/R_eq = 1/24 + 1/72
10. Two resistors of 12 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 12 Ω, R₂ = 3 Ω · R_eq = R₁ + R₂ = ?
11. Two resistors of 18 Ω and 90 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 18 Ω ∥ 90 Ω · 1/R_eq = 1/18 + 1/90
12. Two resistors of 12 Ω and 24 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 12 Ω ∥ 24 Ω · 1/R_eq = 1/12 + 1/24

12 questions · Seed 46 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 10-12

Series & parallel resistor networks

Answers and reasoning. Review before teaching.

1. Two resistors of 14 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
31 Ω
In a series circuit, resistances add directly: R_eq = 14 Ω + 17 Ω = 31 Ω.
2. Two resistors of 32 Ω and 96 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
24 Ω
For two parallel resistors, R_eq = (32 × 96) ÷ (32 + 96) = 3072 ÷ 128 = 24 Ω.
3. Two resistors of 48 Ω and 144 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
36 Ω
For two parallel resistors, R_eq = (48 × 144) ÷ (48 + 144) = 6912 ÷ 192 = 36 Ω.
4. Two resistors of 24 Ω and 11 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
35 Ω
In a series circuit, resistances add directly: R_eq = 24 Ω + 11 Ω = 35 Ω.
5. Two resistors of 2 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
16 Ω
In a series circuit, resistances add directly: R_eq = 2 Ω + 14 Ω = 16 Ω.
6. Two resistors of 9 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
15 Ω
In a series circuit, resistances add directly: R_eq = 9 Ω + 6 Ω = 15 Ω.
7. Two resistors of 17 Ω and 24 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
41 Ω
In a series circuit, resistances add directly: R_eq = 17 Ω + 24 Ω = 41 Ω.
8. Two resistors of 3 Ω and 6 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
2 Ω
For two parallel resistors, R_eq = (3 × 6) ÷ (3 + 6) = 18 ÷ 9 = 2 Ω.
9. Two resistors of 24 Ω and 72 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
18 Ω
For two parallel resistors, R_eq = (24 × 72) ÷ (24 + 72) = 1728 ÷ 96 = 18 Ω.
10. Two resistors of 12 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
15 Ω
In a series circuit, resistances add directly: R_eq = 12 Ω + 3 Ω = 15 Ω.
11. Two resistors of 18 Ω and 90 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
15 Ω
For two parallel resistors, R_eq = (18 × 90) ÷ (18 + 90) = 1620 ÷ 108 = 15 Ω.
12. Two resistors of 12 Ω and 24 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
8 Ω
For two parallel resistors, R_eq = (12 × 24) ÷ (12 + 24) = 288 ÷ 36 = 8 Ω.

12 questions · Seed 46 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Series & parallel resistor networks

Take your time. Show your thinking.

1. Two resistors of 14 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 14 Ω, R₂ = 17 Ω · R_eq = R₁ + R₂ = ?
2. Two resistors of 32 Ω and 96 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 32 Ω ∥ 96 Ω · 1/R_eq = 1/32 + 1/96
3. Two resistors of 48 Ω and 144 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 48 Ω ∥ 144 Ω · 1/R_eq = 1/48 + 1/144
4. Two resistors of 24 Ω and 11 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 24 Ω, R₂ = 11 Ω · R_eq = R₁ + R₂ = ?
5. Two resistors of 2 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 2 Ω, R₂ = 14 Ω · R_eq = R₁ + R₂ = ?
6. Two resistors of 9 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 9 Ω, R₂ = 6 Ω · R_eq = R₁ + R₂ = ?
7. Two resistors of 17 Ω and 24 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 17 Ω, R₂ = 24 Ω · R_eq = R₁ + R₂ = ?
8. Two resistors of 3 Ω and 6 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 3 Ω ∥ 6 Ω · 1/R_eq = 1/3 + 1/6
9. Two resistors of 24 Ω and 72 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 24 Ω ∥ 72 Ω · 1/R_eq = 1/24 + 1/72
10. Two resistors of 12 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 12 Ω, R₂ = 3 Ω · R_eq = R₁ + R₂ = ?
11. Two resistors of 18 Ω and 90 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 18 Ω ∥ 90 Ω · 1/R_eq = 1/18 + 1/90
12. Two resistors of 12 Ω and 24 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 12 Ω ∥ 24 Ω · 1/R_eq = 1/12 + 1/24

12 questions · Seed 46 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Series & parallel resistor networks

Answers and reasoning. Review before teaching.

1. Two resistors of 14 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
31 Ω
In a series circuit, resistances add directly: R_eq = 14 Ω + 17 Ω = 31 Ω.
2. Two resistors of 32 Ω and 96 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
24 Ω
For two parallel resistors, R_eq = (32 × 96) ÷ (32 + 96) = 3072 ÷ 128 = 24 Ω.
3. Two resistors of 48 Ω and 144 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
36 Ω
For two parallel resistors, R_eq = (48 × 144) ÷ (48 + 144) = 6912 ÷ 192 = 36 Ω.
4. Two resistors of 24 Ω and 11 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
35 Ω
In a series circuit, resistances add directly: R_eq = 24 Ω + 11 Ω = 35 Ω.
5. Two resistors of 2 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
16 Ω
In a series circuit, resistances add directly: R_eq = 2 Ω + 14 Ω = 16 Ω.
6. Two resistors of 9 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
15 Ω
In a series circuit, resistances add directly: R_eq = 9 Ω + 6 Ω = 15 Ω.
7. Two resistors of 17 Ω and 24 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
41 Ω
In a series circuit, resistances add directly: R_eq = 17 Ω + 24 Ω = 41 Ω.
8. Two resistors of 3 Ω and 6 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
2 Ω
For two parallel resistors, R_eq = (3 × 6) ÷ (3 + 6) = 18 ÷ 9 = 2 Ω.
9. Two resistors of 24 Ω and 72 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
18 Ω
For two parallel resistors, R_eq = (24 × 72) ÷ (24 + 72) = 1728 ÷ 96 = 18 Ω.
10. Two resistors of 12 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
15 Ω
In a series circuit, resistances add directly: R_eq = 12 Ω + 3 Ω = 15 Ω.
11. Two resistors of 18 Ω and 90 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
15 Ω
For two parallel resistors, R_eq = (18 × 90) ÷ (18 + 90) = 1620 ÷ 108 = 15 Ω.
12. Two resistors of 12 Ω and 24 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
8 Ω
For two parallel resistors, R_eq = (12 × 24) ÷ (12 + 24) = 288 ÷ 36 = 8 Ω.

12 questions · Seed 46 · Age guidance, not curriculum certification